Ninety years before the events of the books, Tya Lannister and Gowen Baratheon (third son of the reigning Lord of Storm's End) were married and produced only one child, a son who died in infancy (I: 406)

Thirty years prior to the above, a male Lannister took a Baratheon woman to wife, producing three daughters and a son (I: 406)

House Baratheon was created in the Wars of Conquest. Its founder was Orys Baratheon, reputed to be a bastard brother of Aegon the Conqueror. Rising through the ranks swiftly, Orys became one of Aegon's fiercest commanders (I: 676)

When Orys Baratheon slew Argilac the Arrogant, the last Storm King, Aegon gave Orys Argilac's castle, lands, and daughter. Orys wed the daughter and took the banner, honors, and words of her line. Baratheon was his own family name, however (I: 676. SSM: 1)

King Harwyn Hardhand of the Iron Islands took the Trident from Arrec the Storm King whose ancestors had won lands up to the Neck three hundred years earlier by killing the last River King (I: 684)

Around 199, Lord Baratheon held a hastilude to celebrate the birth of a grandson (THK: 485)

Ser Lyonel Baratheon was a famed knight in (HK), known as the Laughing Storm (THK: 491)

Lord Steffon Baratheon and his wife were sent by King Aerys across the Narrow Sea to the Free Cities, in search of a suitable bride of sufficiently high lineage and with some Valyrian descent for the sisterless Rhaegar. There they found a splendid young fool whom they bought and were bringing to Storm's End when their ship was smashed in sight of castle and their two eldest sons. Lord Steffon and his wife perished, along with a hundred others. The fool, called Patchface, survived (II: 5. SSM: 1)

Storm's End has warred against Dorne for a thousand years (II: 233)

There are blood ties between Storm's End and the Targaryens, related to marriages some hundred year's past. Most recently, they have Targaryen blood from their descent from Aegon V's daughter, Rhaelle, who was mother to Lord Steffon. These ties were used as justification for Robert Baratheon's ascension to the throne after the rebellion (II: 258. IV: 522. SSM: 1)

The songs say that Storm's End was raised in ancient days by Durran, the First Storm King who had won the love of Elenei, the daughter of the sea god and the goddess of the wind. (II: 345)

It's said that Storm's End has stood for tens of centuries (II: 345)

Storm's End is ancient, its stones woven with spells so that no magic can pass. The spells are forgotten, but still In place (II: 455)

At a tourney at Storm's End when he was young, Prince Rhaegar defeated Lord Steffon Baratheon, Lord Jason Mallister, the Red Viper of Dorne. He broke twelve lances against Ser Arthur Dayne that day, but lost to another knight of the Kingsguard in the final tilt (III: 485. SSM: 1)

Baelor Breakspear led a host of stormlords and Dornishmen at the Redgrass Field, where they shattered the enemy by charging into the rebel rear (TSS: 112)

As a youth, Robert Baratheon would have occasionally visited the Storm's End or travelled outside of the Vale with Jon Arryn. When he reached his majority, his stays in the stormlands were more frequent, but he would have visited the Vale often as it had become a second home to him, and Jon Arryn a second father (SSM: 1)